Numerical models of several processes (for example, physical, chemical, geo-mechanical, etc.) are frequently used in the oil and gas industry to optimize petroleum exploration and production activities. These numerical models are frequently used to identify and screen new prospects, to optimize recovery mechanisms, and to design optimal surface facilities, hence improving net present values (NPV). The challenge of optimizing exploration and production activities using numerical modeling is in having accurate model predictions with acceptable uncertainty tolerance for use in the decision making process. Unfortunately, predictions from current process-based numerical models include major uncertainties; meaning any decision-making process is inherently risky and often results in increased petroleum exploration and production costs.